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SIGMA, 2016, Volume 12, 099, 22 pages (Mi sigma1181)  

This article is cited in 8 scientific papers (total in 8 papers)

Multiple actions of the monodromy matrix in $\mathfrak{gl}(2|1)$-invariant integrable models

Arthur Hutsalyuka, Andrii Liashykbc, Stanislav Z. Pakuliakad, Eric Ragoucye, Nikita A. Slavnovf

a Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region, Russia
b Bogoliubov Institute for Theoretical Physics, NAS of Ukraine, Kyiv, Ukraine
c National Research University Higher School of Economics, Russia
d Laboratory of Theoretical Physics, JINR, Dubna, Moscow region, Russia
e Laboratoire de Physique Théorique LAPTh, CNRS and USMB, Annecy-le-Vieux, France
f Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia

Abstract: We study $\mathfrak{gl}(2|1)$ symmetric integrable models solvable by the nested algebraic Bethe ansatz. Using explicit formulas for the Bethe vectors we derive the actions of the monodromy matrix entries onto these vectors. We show that the result of these actions is a finite linear combination of Bethe vectors. The obtained formulas open a way for studying scalar products of Bethe vectors.

Keywords: algebraic Bethe ansatz; superalgebras; scalar product of Bethe vectors.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 5-100
National Academy of Sciences of Ukraine F14-2016
Russian Foundation for Basic Research 16-01-00562_a
15-31-20484_mol_a_ved
14-01-00860_a
The work of A.L. has been funded by the Russian Academic Excellence Project 5-100 and by joint NASU-CNRS project F14-2016. The work of S.P. was supported in part by the RFBR grant 16-01-00562-a. N.A.S. was supported by the grants RFBR-15-31-20484-mol-a-ved and RFBR-14-01-00860-a.


DOI: https://doi.org/10.3842/SIGMA.2016.099

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Full text: http://www.emis.de/.../099
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ArXiv: 1605.06419
MSC: 82B23; 81R12; 81R50; 17B80
Received: June 24, 2016; in final form October 3, 2016
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Citation: Arthur Hutsalyuk, Andrii Liashyk, Stanislav Z. Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Multiple actions of the monodromy matrix in $\mathfrak{gl}(2|1)$-invariant integrable models”, SIGMA, 12 (2016), 099, 22 pp.

Citation in format AMSBIB
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\paper Multiple actions of the monodromy matrix in $\mathfrak{gl}(2|1)$-invariant integrable models
\jour SIGMA
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\vol 12
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    This publication is cited in the following articles:
    1. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 1. Super-analog of Reshetikhin formula”, J. Phys. A-Math. Theor., 49:45 (2016), 454005, 1–28  crossref  mathscinet  isi
    2. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Form factors of the monodromy matrix entries in $\mathfrak{gl}(2|1)$-invariant integrable models”, Nucl. Phys. B, 911 (2016), 902–927  crossref  mathscinet  zmath  isi
    3. A. A. Hutsalyuk, A. Liashyk, S. Z. Pakulyak, E. Ragoucy, N. A. Slavnov, “Current presentation for the super-Yangian double $DY(\mathfrak{gl}(m|n))$ and Bethe vectors”, Russian Math. Surveys, 72:1 (2017), 33–99  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. Jan Fuksa, “Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry”, SIGMA, 13 (2017), 015, 17 pp.  mathnet  crossref
    5. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation”, J. Phys. A-Math. Theor., 50:3 (2017), 034004  crossref  mathscinet  zmath  isi  elib  scopus
    6. N. Gromov, F. Levkovich-Maslyuk, “New compact construction of eigenstates for supersymmetric spin chains”, J. High Energy Phys., 2018, no. 9, 085  crossref  isi  scopus
    7. S. Belliard, N. A. Slavnov, B. Vallet, “Scalar product of twisted XXX modified Bethe vectors”, J. Stat. Mech.-Theory Exp., 2018, 093103  crossref  isi  scopus
    8. N. A. Slavnov, “Determinant representations for scalar products in the algebraic Bethe ansatz”, Theoret. and Math. Phys., 197:3 (2018), 1771–1778  mathnet  crossref  crossref  adsnasa  isi  elib
  • Symmetry, Integrability and Geometry: Methods and Applications
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